status of little higgs models in 2015reuter/downloads/2015_annecy.pdf1/32j. r. reuter little higgs...

1/32 J. R. Reuter Little Higgs Models LAPTh, Annecy 26.03.2015

Status of Little Higgs Models in 2015

Jürgen R. Reuter

DESY

JRR/Tonini/de Vries, JHEP 1402 (2014) 053; arXiv:1307.5010; JRR/Tonini, JHEP 1302(2013) 077; Kilian/JRR/Rainwater PRD 74 (2006), 095003; PRD 71 (2005), 015008;

Kilian/JRR PRD 70 (2004), 015004

Seminar, LAPTh, Annecy-le-Vieux, 26.03.2015


Standard Model Triumph:§ 2012: Discovery of a Higgs boson

[GeV]Hm

110 115 120 125 130 135 140 145 150

0L

oca

l p

1410

1210

1010

810

610

410

210

1

210

410

510

σ1σ2σ3

σ4

σ5

σ6

σ7

(category)0

Observed p (category)

0Expected p

(inclusive)0

Observed p (inclusive)

0Expected p

= 7 TeVsData 2011, 1

Ldt = 4.8 fb∫ = 8 TeVsData 2012,

1Ldt = 20.7 fb∫

ATLAS Preliminary

γγ→H

100 110 120 130 140 150 160

Eve

nts

/ 2

Ge

V

2000

4000

6000

8000

10000

ATLAS Preliminary

γγ→H

1Ldt = 4.8 fb∫ = 7 TeV, s

1Ldt = 20.7 fb∫ = 8 TeV, s

Selected diphoton sample

Data 2011+2012=126.8 GeV)

HSig+Bkg Fit (m

Bkg (4th order polynomial)

[GeV]γγm100 110 120 130 140 150 160E

ve

nts

F

itte

d b

kg

200

100

0

100

200

300

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500

[GeV]ττm0 100 200 300

[1/

GeV

]ττ

S/B

Wei

gh

ted

dN

/dm

0

200

400

600

800

1000

ττ →H(125 GeV)

observedττ→Z

ttelectroweakQCD

[GeV]ττm100 150

0

20

40ττ →H(125 GeV)

Data - Background

Bkg. Uncertainty

-1 = 7-8 TeV, L = 24.3 fbs CMS Preliminary,

hτhτ, hτµ, hτe, µe

§


No evidence beyond SM ... and what now?


Doubts on the Standardmodel– describes microcosm (too good?)

– 28 free parameters

– Higgs ?, form of Higgs potential ?

measσ) / meas Ofit

(O

3 2 1 0 1 2 3

)2

Z(M

(5)

hadα∆

tm

bm

cm

b

0R

c

0R

0,b

FBA

0,c

FBA

bA

cA

)FB

(Qlept

effΘ

2sin

(SLD)l

A

(LEP)l

A

0,l

FBA

lep

0R

0

hadσ

ZΓ

ZM

WΓ

WM

HM

0.1

0.4

0.0

0.0

2.4

0.0

2.5

0.9

0.6

0.0

0.7

1.9

0.2

0.8

1.1

1.7

0.1

0.2

0.2

1.2

0.0G fitter SM

Sep 12

250

500

750

103 106 109 1012 1015 1018

MH [GeV]

Λ[GeV]

Hierarchy Problemchiral symmetry: δmf9v lnpΛ2v2q

no symmetry for quantum corrections toHiggs mass

δM2H9Λ2 „M2

Planck “ p1019q2 GeV2

p125 GeVq2 = ( 1000000000000000000000000000000020000 –

1000000000000000000000000000000000000 ) GeV2


Electroweak vacuum stability

§ Recent analysis: Metastable vacuum with lifetime longer than the ageof the universe Degrassi et al., arXiv:1205.6497

0 50 100 150 2000

50

100

150

200

Higgs mass Mh in GeV

Top

mas

sM

tin

GeV

Instability

Non

-perturbativity

Stability

Meta-stab

ilityInstability

107

109

1010

1012

115 120 125 130 135165

170

175

180

Higgs mass Mh in GeVP

ole

top

mas

sM

tin

GeV

1,2,3 Σ

Instability

Stability

Meta-stability

§ Could the Higgs field ever have fallen in the correct vacuum?Hertzberg, arXiv:1210.3624

§ Importance of higher terms in Higgs potential (gravity etc.) ?




102 104 106 108 1010 1012 1014 1016 1018 1020

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

RGE scale Μ in GeV

Hig

gsqu

arti

cco

upli

ngΛH

ΜL

Mh = 125 GeV3Σ bands in

Mt = 173.1 ± 0.7 GeVΑsHMZL = 0.1184 ± 0.0007

Mt = 171.0 GeV

ΑsHMZL = 0.1163

ΑsHMZL = 0.1205

Mt = 175.3 GeV

102 104 106 108 1010 1012 1014 1016 1018 1020

0.0

0.2

0.4

0.6

0.8

1.0

RGE scale Μ in GeV

SMco

uplin

gs

g1

g

gsyt

Λyb




Higgs as Pseudo-Goldstone boson

Nambu-Goldstone Theorem: For each spontaneously broken globalsymmetry generator there is a massless boson in the spectrum.

Old idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984

Light Higgs as (Pseudo)-Goldstone boson of a spontaneouslybroken global symmetry

Λ

v

O(1 GeV)

O(150 MeV)

Analogous: QCDScale Λ: chiral symmetrybreaking, quarks, SUp3qcScale v: pions, kaons, . . .

Without Fine-Tuning: experimentally excluded


Higgs as Pseudo-Goldstone boson

Nambu-Goldstone Theorem: For each spontaneously broken globalsymmetry generator there is a massless boson in the spectrum.

Old idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984

Light Higgs as (Pseudo)-Goldstone boson of a spontaneouslybroken global symmetry

Λ

v

O(1 TeV)

O(250 GeV)

Scale Λ: global symmetrybreaking, new particles, new(gauge) IAScale v: Higgs, W Z, `˘, . . .

Without Fine-Tuning: experimentally excluded


Collective symmetry breaking and 3-scale models

Collective symmetry breaking: Arkani-Hamed/Cohen/Georgi/Nelson/. . . , 2001

2 different global symmetries; one of them unbroken ñ Higgsexact Goldstone boson

Coleman-Weinberg: boson masses by radia-tive corrections, but: mH only at 2-loop level mH „

g1

4π

g2

4πΛ

Λ

F

v

O(10 TeV)

O(1 TeV)

O(250 GeV)

Scale Λ: global SB, new IAScale F : Pseudo-Goldstonebosons, new vectors/fermionsScale v: Higgs, W Z, `˘, . . .


Characteristics and Spectra

Λ

F

v

O(& 10 TeV)

O(1 TeV)

O(250 GeV)

Scale Λ: “hidden sector”,symmetry breaking

Scale F : new particles

Scale v: h, W Z, `˘, . . .

Terascale: new particles to stabilize the hierarchy

h

H,A H±

τ1˜R

ν`˜L

τ2

t2qR

b2b1

t1

qL

χ04, χ±2

tχ01

g

χ03

SUSY

χ02, χ±1

0.25

0.50

0.75

1.00

1.25

M [TeV]

h

Little Higgs

ΦP

Φ±Φ±±

Φ

ηW± Z

γ′

W ′ ±Z′ T

t

U,C


Generic properties of Little-Higgs models– Extended global symmetry (extended scalar sector)

– Specific functional form of the potential

– Extended gauge symmetry: γ1 ” AH , Z1 ” ZH ,W

1 ˘ ”WH

– New heavy fermions: T , but also U,C, . . .

Product Group Models(e.g. Littlest Higgs)

H → H′

G1 → G′1 G2 → G′1[H1,H2] 6= 0

/H1 ⊂ H /H2 ⊂ Hg1 6= 0 g2 6= 0

Simple Group Models(e.g. Simplest Little Higgs)

H1 → H′1 H2 → H′

2

Gdiag → G′

H1 3 h ∈ H2

‚ discrete T (TeV) parity: pair production, cascades, DM


Generic properties of Little-Higgs models– Extended global symmetry (extended scalar sector)

– Specific functional form of the potential

– Extended gauge symmetry: γ1 ” AH , Z1 ” ZH ,W

1 ˘ ”WH

– New heavy fermions: T , but also U,C, . . .

Product Group Models(e.g. Littlest Higgs)

H → H′

G1 → G′1 G2 → G′1[H1,H2] 6= 0

/H1 ⊂ H /H2 ⊂ Hg1 6= 0 g2 6= 0

Quiver [Moose] Models(e.g. Minimal Moose Model)

• • •

• • •

/H1 /H2 /H3 /H4 /H5 /Hn

/G1 /G2 /G3 /G4 /Gn

‚ discrete T (TeV) parity: pair production, cascades, DM


Prime Example: Simple Group Model§ enlarged gauge group: SUp3q ˆ Up1q; globally Up3q Ñ Up2q

§ Two nonlinear Φ representations L “ |DµΦ1|2 ` |DµΦ2|

2

Φ12 “ exp

„

˘if21

f12Θ

¨

˝

0

0

f12

˛

‚ Θ “1

a

f21 ` f

22

¨

˝

η 0

0 ηh˚

hT η

˛

‚

Coleman-Weinberg mechanism: Radiative generation of potential

` “g2

16π2Λ2

`

|Φ1|2 ` |Φ2|

2˘

„g2

16π2f2

but:Φ1

Φ:1

Φ2

Φ:2“

g4

16π2log

ˆ

Λ2

µ2

˙

|Φ:1Φ2|2 ñ

g4

16π2log

ˆ

Λ2

µ2

˙

f2ph:hq


Indirect constraints: Higgs/EW precision

How to constrain a generic model in HEP?

§ direct searches of resonances§ electroweak precision tests§ flavour constraints§ nowadays: Higgs sector

Higgs sector is the key to understand EW-scale physics (and beyond?)


Statistical analysis

We considered the three most popular Little Higgs models:§ Simplest Little Higgs (SLH) [Schmaltz]

§ Littlest Higgs (L2H) [Arkani-Hamed et al.]

§ Littlest Higgs with T-parity (LHT) [Low et al.]

and realized a χ2 analysis on their parameter spaces, taking into accountthe whole set of 7+8 TeV Higgs searches by ATLAS and CMS, and byfitting 21 different EW Precision Observables:

χ2 “ÿ

i

`

Oi ´Oexpi

˘2

σ2i

where Oi depends on the free parameters of the model considered.


Data used: Higgs sectorthe Higgs results are expressed in terms of a signal strength modifier

µi “

ř

p εpi σp

ř

p εpi σ

SMp

¨BR phÑ XiXiq

BR phÑ XiXiqSM

we included in our χ2 analysis the best-fit values of µi reported by theCollaborations for all the different 7+8 TeV channels i:


Data used: EWPD

every extension of SM has to satisfy at leastthe precision constraints of the electroweaksector:

§ low-energy observables

e.g. ν-scattering, parity violation observables...

§ Z-pole observables

e.g. mZ , ΓZ , Z-pole asymmetries...


LH Smoking guns

Where do the LH corrections to the SM quantities come from?

§ new decay channels of the Higgs, e.g. hÑ AHAH in LHT§ modified Higgs couplings with SM fermions and vector bosons

e.g. 2m2W

vyW hW`W´, yW “

#

1 SM

1`O`

v2f2˘

LH

§ interaction terms of Higgs with new fermions/vector bosons

e.g.mT

vyT h T T mT „ f, yT „ O

`

v2f2˘

§ modified neutral- and charged-currents

e.g.g

cW

ÿ

f

fγµ´

pgSML ` δgLqPL ` pgSMR ` δgRqPR

¯

f Zµ


SLH results JRR/Tonini, JHEP 1302 (2013) 077; JRR/Tonini/de Vries, JHEP 1402 (2014) 053

χ2mind.o.f. “ 1.043

χ2SMd.o.f. “ 1.048

§ free parameters: f SSB scale, tβ ratio ofvevs of scalar fields φ1,2

§ f99%min “ 2.88 TeV, translates into lower

bounds on new states’ masses, e.g.

mW 1 Á 1.35 TeV

mT Á 2.81 TeV

§ min. required fine tuning: „ 1%, defined as

∆ “|δµ2

|

µ2obs

§ results mainly driven by EWPD§ includes data from Moriond 2013


L2H results JRR/Tonini, JHEP 1302 (2013) 077; JRR/Tonini/de Vries, JHEP 1402 (2014) 053

χ2mind.o.f. “ 1.048

χ2SMd.o.f. “ 1.049

§ free parameters: f SSB scale, c mixingangle in gauge sector

§ f99%min “ 3.20 TeV, translates into lower


mW 1 Á 2.13 TeV

mT Á 4.50 TeV

§ min. required fine tuning: „ 0.1%, defined as

∆ “|δµ2

|

µ2obs

§ results mainly driven by EWPD§ includes data from Moriond 2013§ Exclusion gets weaker by Higgs data (d.o.f.)!


LHT: Littlest Higgs with T parity

§ Goldstone boson matrix:

Σ “ e2 iΠf Π “1?

2

¨

˝

0 H?

2Φ

H: 0 Ht?

2Φ: H˚ 0

˛

‚ Φ9

ˆ?

2φ`` φ`

φ` φ0 ` i φP

˙

§ Discrete T parity:

T : Π Ñ ´Ω Π Ω Ω “ diagp1, 1,´1, 1, 1q

§ Yukawa couplings k,R ” λ1λ2

Lk “´ kf´

Ψ2ξΨc ` Ψ1xΣyΩξ:ΩΨc

¯

´mq u1c uc ´mq d

1c dc ´mχ χ

1c χc + h.c.

Lt “´λ1f

2?

2εijk εxy

”

`

Ψ1,t

˘

iΣjx Σky ´

`

Ψ2,t xΣy˘

iΣ1jx Σ1ky

ı

t1R ´ λ2f`

TL1TR1

` TL2TR2

˘

+ h.c.


T parity/Dark Matter Cheng/Low, 2003; Hubisz/Meade, 2005; Wang/Yang/Zhu, 2013

§ T parity: T a Ñ T a, Xa Ñ ´Xa, automorphism of coset spaceanalogous to R parity in SUSY, KK parity in extra dimensions

§ Bounds on F MUCH relaxed, F „ 0.5´ 1 TeVbut: Pair production!, typical cascade decays

§ Lightest T -odd particle (LTP) ñ Candidate for Cold Dark Matter

Littlest Higgs: A1 LTP

W 1, Z1 „ 650 GeV, Φ „ 1 TeVT, T 1 „ 0.7-1 TeV

Annihilation: A1A1 Ñ hÑWW,ZZ, hh

§ T parity Simplest LH: Pseudo-Axion η LTPZ 1 remains odd: good or bad (?) Martin, 2006

§ T parity might be anomalous (???) Hill/Hill, 2007







W 1, Z1 „ 650 GeV, Φ „ 1 TeVT, T 1 „ 0.7-1 TeV


Hubisz/Meade, 2005

0/10/50/70/100600 800 1000 1200 1400 1600 1800 2000

100

200

300

400

500108 144 180 216 252 288

MH(GeV)

M (GeV)AH

f

f (GeV)









W 1, Z1 „ 650 GeV, Φ „ 1 TeVT, T 1 „ 0.7-1 TeV


Wang/Yang/Zhu, 2013

Relic density/SI cross section50 100 150 200 250 300 350 4007

8

9

10

11

12

13

14

15

16 2258.71624.7998.8

MAH(GeV)

M=M

H-M

AH(G

eV)

0.1064

0.1118

0.1172

0.1226

0.1280

0.1334

f (GeV)ch

2

2576.91941.21310.0695.1









W 1, Z1 „ 650 GeV, Φ „ 1 TeVT, T 1 „ 0.7-1 TeV


Wang/Yang/Zhu, 2013

Relic density/SI cross section10

-3

10-2

10-1

1

10

0 100 200 300 400 500 600

LHT-A best point

XENON100(2012)

XENON1T(2017)

M (GeV)AH

695.1 1310.0 1941.2 2576.9

412.2 998.8 1624.7 2258.7

3214.5 3853.1

2895.6 3533.7

f (GeV)

σS

I (

×10

-44 c

m2)




LHT results JRR/Tonini, JHEP 1302 (2013) 077; JRR/Tonini/de Vries, JHEP 1402 (2014) 053

χ2mind.o.f. “ 1.048

χ2SMd.o.f. “ 1.053

§ free parameters: f SSB scale, R ratio ofYukawa couplings in top sector

§ f99%min “ 405.9 GeV, translates into lower


mW 1 Á 269.6 GeV

mT Á 553.6 GeV

§ min. required fine tuning: „ 10%, defined as

∆ “|δµ2

|

µ2obs

§ results mainly driven by EWPD (see nextslide)

EWPT ñ f Á 405 GeV


Higgs data vs. EWPD

§ the shape of result driven by EW constraints (much smaller uncertainties)§ Higgs data only: for vf Á 0.6 decay hÑ AHAH open and dominant§ Higgs data only: subdominant dependence on R w.r.t. f is a consequence of

the Collective Symmetry Breaking mechanism

EWPT and Higgs data ñ f Á 694 GeV


Direct searches: Drell-Yan mainly

Reach in the gauge boson sector: depends on mixing angle


Direct Searches: Focus on LHT

§ Defining two benchmark scenarios: 1. heavy quarks



§ Defining two benchmark scenarios: 2. heavy top/vectors



§ Defining two benchmark scenarios: 1. k “ 1.5, 2. k “ 0.4


Branching Ratios§ Decay patterns:

Particle Decay BRk“1.0 BRk“0.4

l˘H W˘

H ν 62% 0%ZH l

˘ 31% 0%AH l

˘ 6% 100%

ν˘H W˘

H l¯ 61% 0%ZH ν 30% 0%AH ν 9% 100%

T`H W` b 46% 45%Z t 22% 22%H t 21% 21%T´H AH 11% 11%

AH stable

ZH AH H 100% 2%dH d 0% 41%uH u 0% 30%l˘H l¯ 0% 14%νH ν 0% 14%

Particle Decay BRk“1.0 BRk“0.4

dH W´

H u 62% 0%ZH d 30% 0%AH d 6% 100%

uH W`

H d 58% 0%ZH u 30% 0%AH u 9% 100%

T´H AH t 100% 100%ZH t 0% 0%

Φ0P AH H 100% 100%

Φ˘ AH W˘ 100% 100%

Φ˘˘ AH pW˘q2 100% 96%

W˘

H AH W˘ 100% 2%

uH d 0% 44%dH u 0% 27%l˘H ν 0% 16.5%νH l

˘ 0% 16.5%


Cross Sections (I)§ Heavy Quarks

§ Heavy Top and Vectors


Channels and signatures: Parameters

final state modes paramsleptons # jets ET

0 1 3 qHAH f, k

0 2 3 qHqH f, k

0 3 3 qHW˘

H f, k

0 4 3

qHqH f, k

W˘

H W¯

H f, k

W˘

H ZH f, k

ZHZH f, k

0 4 7 T`q f, k, R

0 5 3 qHW˘

H f, k

0 6 3qHqH f, k

T´T´ f, k, R

final state modes paramsleptons # jets ET

l˘ 2 3W˘

H W¯

H f, k

W˘

H ZH f, k

qHqH f, k

l˘ 3 3qHW

˘

H f, k

T`q f, k, R

l˘ 4 3qHqH f, k

T´T´ f, k, R

l`l´ 0 3 W˘

H W¯

H f, k

l`l´ 1 3 qHW˘

H f, k

l`l´ 2 3qHqH f, k

T´T´ f, k, R

l˘l˘ 2 3 qHqH f, k


Channels and signatures (I)

final state production

modes

σ8 TeV ˆ Br pfbq σ14 TeV ˆ Br pfbq

# l˘ # jets ET k “ 1.0 k “ 0.4 k “ 1.0 k “ 0.4

0 1 3 qHAH 0.24 1.1ˆ102 2.1 4.5ˆ102

0 2 3 qHqH 0.56 5.6ˆ103 5.2 3.2ˆ104

0 3 3qHW

˘

H 0.73 14 8.0 77

qHZH 0.76 8.6 8.0 49

0 4 3

qHqH 4.0 9.1ˆ102 35 5.6ˆ103

W˘

H W¯

H 1.9 low 9.1 lowW˘

H ZH 4.8 low 23 lowZHZH 0.56 low 3.0 low

0 4 7 T`q 2.0 2.0 17 17

0 5 3qHW

˘

H 5.1 7 54 7

qHZH 4.1 7 44 7

0 6 3qHqH 1.6 9.7ˆ102 1.7ˆ102 6.0ˆ103

T´T´ 2.5 2.5 25 25


Channels and signatures (II)

final state production

modes

σ8 TeV ˆ Br pfbq σ14 TeV ˆ Br pfbq

# l˘ # jets ET k “ 1.0 k “ 0.4 k “ 1.0 k “ 0.4

l˘ 2 3

qHqH 0.058 9.0ˆ102 1.1 5.6ˆ103

W˘

H W¯

H 0.77 low 3.9 lowW˘

H ZH 2.1 low 10 lowT`q 1.3 1.2 10 10

l˘ 3 3qHW

˘

H 3.5 7 37 7

qHZH 0.99 7 11 7

l˘ 4 3qHqH 7.4 9.7ˆ102 82 6.0ˆ103

T´T´ 2.2 2.2 21 21

l`l´ 0 3 W˘

H W¯

H 0.32 low 1.7 low

l`l´ 1 3 qHW˘

H 0.54 7 5.8 7

l`l´ 2 3qHqH 1.1 7 11 7

T´T´ 0.47 0.47 4.6 4.6

l˘l˘ 2 3 qHqH 0.37 7 2.7 7


Recasting results JRR/Tonini/deVries,2013

‚ 95% CL from Monojets + ET from LHC8‚ 1 hard jet, ET , no leptons, 2nd jet w. pT ą 30 GeV

signal regions: ATLAS ppT , ET q ą 120/220/350/500 GeV, CMS: ET ą 250/300/350/400/450/500/550 GeV

‚ Dijet suppression: ATLAS ∆φp ET , j2q ą 0.5, CMS ∆φpj1, j2q ă 2.5

‚ ppÑ qHqH , ppÑ qHAH



‚ 95% CL from Jets + ET from LHC8‚ ě 2 hard jets, ET , no leptons

‚ signal regions: ATLAS ET ą 200/300/350 GeV, CMS:

pNj , Nbq “ p2´ 3, 0q; p2´ 3, 1´ 2q; pě 4, 1´ 2q; pě 4, 0q; pě 4,ě 2q

‚ QCD suppression: ATLAS ∆φp ET , j2q ą 0.5, ET meff , CMS ∆φpj1, j2q ă 2.5

‚ ppÑ qHqH Ñ pjAHqpjAHq



‚ 95% CL from Leptons + Jets + ET from LHC8‚ single isolated lepton, ě 2 hard jets, ET ,

‚ signal regions: ATLAS ET ą 200/300/350 GeV

‚ Cuts: ET ą 250 GeV, mT pl, ET q ą 250 GeV, ET meff ą 0.2, minceff ą 800 GeV

‚ ppÑ qHqH with qH ÑWHq, ZHq, tH Ñ tAH , ZH Ñ HAH


Combined analysis JRR/Tonini/deVries,2013

§ Operator bounds: O4-f “ ´k2

128π2f2ψLγ

µψLψ1Lγµψ

1L `O

` gk

˘

Hubisz/Meade/Noble/Perelstein, 2005

§ Bound from combined analysis: f Á 638GeV


Conclusions§ Little Higgs models are an appealing solution to the hierarchy

problem, alternative to weakly coupled solutions like SUSY

§ most of the parameter space of three popular Little Higgs models isstill compatible at „ 99% CL with the early results of the 7+8 TeVHiggs searches

§ electroweak precision data represent still the most severe constraints

§ fine-tuning as a guideline to understand the naturalness of a model:Little Higgs models require a minimum level of „ 10% of fine tuning

§ Limits on the LHT:1. EWPO: f Á 405 GeV@95% CL

2. Higgs: f Á 607 GeV@95% CL

3. Higgs+EWPO: f Á 694 GeV@95% CL

4. Direct searches: f Á 638 GeV@95% CL

§ We need more data!


One Ring to Find them ... One Ring to Rule them Out


BACKUP SLIDES:


Direct Searches – Heavy Quark States§ EW single dominates QCD pair production: Perelstein/Peskin/Pierce, ’03

§ Characteristic branching ratios :

ΓpT Ñ thq « ΓpT Ñ tZq «1

2ΓpT Ñ bW`q «

MTλ2T

64π, ΓT „ 10´50 GeV

§ Proof of T as EW singlet; but: T Ñ Z 1T,W 1b, tη !

AIM: Determination of MT , λT , λT 1 λT 1 indirect (T Th impossible)


T Ñ ZtÑ ```´`νb SN-ATLAS-2004-038

—————————————————§ ET ą 100 GeV, ```, pT ą 10030 GeV,b, pT ą 30 GeV

§ Bkgd.: WZ,ZZ, btZ

§ Observation for MT À 1.4 TeVInvariant Mass (GeV)

0 500 1000 1500 2000

-1E

vents

/40 G

eV

/300 fb

0.5

1

1.5

2

2.5

3

3.5

4

ATLAS


T ÑWbÑ `νb SN-ATLAS-2004-038

—————————————————§ ET ą 100 GeV, `, pT ą 100 GeV,b, pT ą 200 GeV, max. jj, pT ą 30 GeV

§ Bkgd.: tt,Wbb, single t§ Observation for MT À 2.5 TeV

Invariant Mass (GeV)

0 500 1000 1500 2000

-1E

vents

/40 G

eV

/300fb

50

100

150

200

250

300

350

400

ATLAS


T Ñ thÑ `νbbb SN-ATLAS-2004-038

—————————————————§ `, pT ą 100 GeV, jjj, pT ą 130 GeV,

at least 1 b-tag§ Bkgd.: tt,Wbb, single t§ Observation for MT À 2.5 TeV

0

10

20

30

40

50

500 1000 1500

ATLAS

Mass(jjjeν) (GeV)

Eve

nts/

30 G

eV/3

00 fb

-1





0

10

20

30

40

50

500 1000 1500

ATLAS

Mass(jjjeν) (GeV)

Eve

nts/

30 G

eV/3

00 fb

-1

Additional heavy quarks (Simple Group Models): U,C or D,S Han et al.,

05

§ Large cross section: u or dPDF

§ Huge final state ` chargeasymmetry

§ Good mass reconstruction





0

10

20

30

40

50

500 1000 1500

ATLAS

Mass(jjjeν) (GeV)

Eve

nts/

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eV/3

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05




forward jet

high pT jet

q qQ

W

l ν+−

+−





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500 1000 1500

ATLAS

Mass(jjjeν) (GeV)

Eve

nts/

30 G

eV/3

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-1


05





Direct Searches – Heavy VectorsDrell-Yan Production: Tevatron Limits „ 500´ 600 GeV

§ Dominant decays:Product group: Z 1 Ñ Zh,WW ,W 1 ÑWh,WZSimple group: Z 1 Ñ qq, X Ñ fF

§ Discovery channel: Z 1 Ñ ``, W 1 Ñ `ν

§ ΓZ1 „ 10´ 50 GeV, ΓX „ 0.1´ 10 GeV


Direct Searches – Heavy VectorsDrell-Yan Production: Tevatron Limits „ 500´ 600 GeV

§ Dominant decays:Product group: Z 1 Ñ Zh,WW ,W 1 ÑWh,WZSimple group: Z 1 Ñ qq, X Ñ fF

§ Discovery channel: Z 1 Ñ ``, W 1 Ñ `ν

§ ΓZ1 „ 10´ 50 GeV, ΓX „ 0.1´ 10 GeV

10-1

1

10

10 2

1600 1800 2000 2200 2400mee (GeV)

Even

ts/1

0 G

eV/1

00 fb

-1

ZH cotθ=1.0

ZH cotθ=0.2

Drell-Yan

ATLAS

10-1

1

10

10 2

1000 1500 2000 2500 3000

mT (GeV)

Even

ts/2

0 G

eV/1

00 fb

-1

WH cotθ=0.2

WH cotθ=0.5

Drell-Yan

top

ATLAS


Direct Searches – Heavy Scalars

Generally: Large model dependenceno states complex singlet complex triplet

§ Littlest Higgs, complex triplet:Φ0,ΦP ,Φ

˘,Φ˘˘

§ Cleanest channel: qq Ñ Φ``Φ´´ Ñ ````:Killer: PS

§ WW -Fusion: ddÑ uuΦ`` Ñ uuW`W`

§ 2 hard forward jets, hard close ````

pT -unbalanced 0

2

4

6

8

600 800 1000 1200 1400 mT (GeV)

Eve

nts/

100

GeV

/300

fb-1

mΦ = 1 TeV

ATLAS

Alternative: Model-Independent search in WW fusion:ILC: Beyer/Kilian/Krstonosic/Mönig/JRR/Schmidt/Schröder, 2006

LHC: Alboteanu/Kilian/JRR, 2008; Kilian/JRR/Sekulla, 2013


Pseudo-Axions in Little Higgs Kilian/Rainwater/JRR, 2004, 2006; JRR,

2007

– gauged Up1q group: Z 1 ÐÑ ungauged: η

– couples to fermions like a pseudoscalar

– mη À 400 GeV

– SM singlet, couplings toSM particles vF suppressed

– η axion-like particle:

gg

bb

µ+µ−

cc

τ+τ−

γγ

Zh

50 100 150 200 250 300

10−4

0.001

0.01

0.1

1

mη [GeV]

BR [η]

Anomalous Up1q: ÝÑ 1Fαs8π2 ηFµνFρσε

µνρσ

– Up1q explicitly broken ñ Axion limits from astroparticle physicsnot applicable


Classification of Axions in Little Higgs ModelsNumber of Pseudo-Axions: n “ g ´ lMismatch between global (g) and local rank reduction (l)

Product Group Models Arkani-Hamed,. . .

§ Doubling of electroweak gauge group: SUp2q ˆ SUp2q Ñ SUp2qL,Up1q ˆ Up1q Ñ Up1qY (latter not necessary) ñ l “ 1

§ Littlest Higgs, g: SUp5q Ñ SOp5q ñ n “ p4´ 2q ´ 1 “ 1§ antisymmetric, g: Spp6qSOp6q, n “ p3´ 2q ´ 1 “ 0

Simple Group Models Kaplan,Schmaltz, . . .

§ Simple gauge group: SUpNq ˆ Up1q Ñ SUp2q ˆ Up1q ñ l “ N ´ 2

§ Higgs is distributed over several global symmetry multiplets§ Simplest Little Higgs, g: rSUp3qs2rSUp2qs2 n “ g ´ l “ 2´ 1 “ 1

§ Original Simple Group Model, g: rSUp4qs3rSUp3q3 ˆ SUp2qs,l: SUp4q Ñ SUp2q n “ g ´ l “ 4´ 2 “ 2

Moose Models Arkani-Hamed, . . .

§ “Minimal” Moose: g rSUp3qs4 Ñ SUp3q, l rSUp3q ˆ SUp2qsSUp2qn “ g ´ l “ 6´ 2 “ 4

§ 3-site model: g rSUp2qs4rSUp2qs2, l rSUp2qs2 Ñ SUp2q, n “ 2´ 1 “ 1


ZHη coupling as a discriminator Kilian/Rainwater/JRR, 2006

§ pseudo-axion: ξ “ exp riηF s, Σ “ exp riΠF s non-linearrepresentation of the remaining Goldstone multiplet Π

Lkin. „ F 2 Tr“

pDµpξΣq:pDµpξΣqq‰

“ . . .´2F pBµηq Im Tr“

pDµΣq:Σ‰

Òpη2q

§ Use special structure of covariant derivatives:

DµΣ “ BµΣÀa1,µ`

T a1 Σ` ΣpT a1 qT˘

Àa2,µ`

T a2 Σ` ΣpT a2 qT˘

,

Tr“

pDµΣq:Σ‰

„W aµ Tr

“

Σ:pT a1 ` Ta2 qΣ` pT

a1 ` T

a2 q˚‰

“ 0.

§ Little Higgs mechanism cancels this coupling§ Simple Group Models: Φ “ expriΣF s, ζ “ p0, . . . 0, F qT VEV directing

in the N direction


Lkin. „ F 2Dµpζ:Φ:qDµpΦζq “ . . .ì

FpBµηqζ

:`

Φ:pDµΦq ´ pDµΦ:qΦ˘

ζ

“ . . .` iF pBµηq`

Φ:pDµΦq ´ pDµΦ:qΦ˘

N,N.

Σ “

ˆ

0 h

h: 0

˙

, Vµ “

ˆ

Wµ 0

0 0

˙

` heavy vector fields

Vµ ì

FrΣ,Vµs ´

1

2F 2rΣ, rΣ,Vµss ` . . .

“

ˆ

Wµ 0

0 0

˙

ì

F

ˆ

0 ´Wµh

h:Wµ 0

˙

´1

2F 2

ˆ

hh:W `Whh: 0

0 ´2h:Wh

˙

`. . .

§ 1st term cancels by multiple Goldstone multiplets§ 2st term cancels by EW symmetry§ 3rd term

pBµηqh:Wµh „ vHZµB

µη .


More properties of Pseudo-Axions§ Take e.g. one specific model: Simplest Little Higgs Schmaltz, 2004

§ Simple Group Model, two Higgs-triplets with a tanβ-like mixing angle

tanβ = 1

2

46

mη [GeV]

0 100 200 300 4000

200

400

600

µ [GeV]

tanβ = 1

24

mH [GeV]

F2 = 2 TeV

0 100 200 300 4000

200

400

600

800

µ [GeV]

F1 = 0.5 TeV

1

1.5

2

mH [GeV]

tan β = 4

0 100 200 300 4000

200

400

600

800

µ [GeV]

§ tanβ „ 1: heavy Higgs, (very) light pseudoscalar§ Heavy top decays: Kilian/Rainwater/JRR, 2006


Discovery of Pseudo-axions Kilian/Rainwater/JRR, 2004, 2006

LHC: Gluon fusion, diphotonsignal for mη Á 200 GeV, 7σpossible

LHC: T Ñ tη

ILC: e`e´ Ñ ttη




LHC: T Ñ tη

ILC: e`e´ Ñ ttη

e−e+ → ttbb

#evt/2 GeV

√s = 800 GeV∫L = 1 ab

−1

gttη = 0.2

mη = 50 GeV100

150

0 50 100 150

10

100

1000

10 4

Minv(bb) [GeV]




LHC: T Ñ tη

ILC: e`e´ Ñ ttη

ZHη coupling

forbidden in Product Group Models

Discriminator of diff. model classes

gg Ñ

"

H Ñ Zη Ñ ``bb

η Ñ ZH Ñ ``bb, ```jj

*


η pheno at ILC Kilian/Rainwater/JRR, 2006

If ZHη coupling present: Hη production in analogy to HA:

µ = 150 GeV

97

24.2

σ(e+e− → Z∗ → ηH) [fb]

200 400 600 800 1000 1200

0.2

0.4

0.6

0.8

1

1.2

√s [GeV]

µ = 150 GeV

97

24.2

σ(e+e− → Z∗/Z ′ ∗ → ηH) [fb]

200 400 600 800 1000

0.2

0.4

0.6

0.8

1

1.2

√s [GeV]

§ Light pseudoaxion, η Ñ bb, final state Hbb§ Intermediate range, η Ñ gg, final state Hjj§ η Ñ ZH: ZHH final state

no Z ′with Z ′

SM

σ(e+e− → Hη∗ → Hbb) [fb]

30 < Mbb < 70 GeV

µ = 24 GeV

500 600 700 800 900 1000

0.2

0.4

0.6

0.8

1

1.2

√s [GeV]

no Z ′ with Z ′

SM

σ(e+e− → Hη∗ → Hjj) [fb]

Mjj > 150 GeV

500 600 700 800 900 1000

0.1

0.2

0.3

√s [GeV]

no Z ′

with Z ′

SM

σ(e+e− → η∗H → ZHH) [fb]

400 600 800 1000

0.5

1

1.5

√s [GeV]

More detailed insights from photon collider option


η pheno at ILC Kilian/Rainwater/JRR, 2006

If ZHη coupling present: Hη production in analogy to HA:

µ = 150 GeV

97

24.2

σ(e+e− → Z∗ → ηH) [fb]

200 400 600 800 1000 1200

0.2

0.4

0.6

0.8

1

1.2

√s [GeV]

µ = 150 GeV

97

24.2

σ(e+e− → Z∗/Z ′ ∗ → ηH) [fb]

200 400 600 800 1000

0.2

0.4

0.6

0.8

1

1.2

√s [GeV]

§ Light pseudoaxion, η Ñ bb, final state Hbb§ Intermediate range, η Ñ gg, final state Hjj§ η Ñ ZH: ZHH final state

no Z ′with Z ′

SM

σ(e+e− → Hη∗ → Hbb) [fb]

Mbb > 150 GeV

µ = 97 GeV

500 600 700 800 900 1000

0.2

0.4

0.6

0.8

1

√s [GeV]

no Z ′ with Z ′

SM

σ(e+e− → Hη∗ → Hjj) [fb]

Mjj > 150 GeV

500 600 700 800 900 1000

0.1

0.2

0.3

√s [GeV]

no Z ′

with Z ′

SM

σ(e+e− → η∗H → ZHH) [fb]

400 600 800 1000

0.5

1

1.5

√s [GeV]

More detailed insights from photon collider option


Pseudo Axions at the Photon Collider

§ Photon Collider as precisionmachine for Higgs physics (schannel resonance, anomalycoupling)

λT λT

§ S/B analogous to LC§ η in the µ model with (almost)

identical parameters as A inMSSM( ãÑ Mühlleitner et al. (2001) )

H (SM)H (with T )η [T ]η [1 complete heavy gen.]η [3 gen. of heavy quarks]η [3 complete heavy gen.]

σeff(γγ → η,H) [pb]

100 200 300 400 500 600 700

0.001

0.01

0.1

1

10

mH,mη [GeV]


Pseudo Axions at the Photon Collider

§ Photon Collider as precisionmachine for Higgs physics (schannel resonance, anomalycoupling)

λT F

§ S/B analogous to LC§ η in the µ model with (almost)

identical parameters as A inMSSM( ãÑ Mühlleitner et al. (2001) )

H (SM)H (with T )η [T ]η [1 complete heavy gen.]η [3 gen. of heavy quarks]η [3 complete heavy gen.]

σeff(γγ → η,H) [pb]

100 200 300 400 500 600 700

0.001

0.01

0.1

1

10

mH,mη [GeV]


gbbη “ 0.4 ¨ gbbhmη 100 130 200 285

ΓγγrkeVs 0.15 0.27 1.1 3.6

γγ → (H,η) → bb

#evt/2 GeV

√see = 200 GeV

∫Lee = 400 fb

−1

| cos(θ)T | < 0.76

|pz|/√see < 0.1

mη =

100 GeV

130

80 100 120 140 1600

200

400

600

800

1000

1200

1400

Minv(bb) [GeV]

γγ → (H,η) → bb

#evt/2 GeV

√see = 500 GeV

∫Lee = 1 ab

−1

| cos(θ)T | < 0.76

|pz|/√see < 0.04

mη = 200 GeV

285

100 200 300 400

10

100

1000

104

Minv(bb) [GeV]


Simplest Little Higgs (“µ Model”) Schmaltz ’04, Kilian/Rainwater/JRR ’04

Field content (SUp3qc ˆ SUp3qw ˆ Up1qX quantum numbers)

Φ1,2 : p1, 3q´ 13

Ψ` : p1, 3q´ 13

u1,2c : p3, 1q´ 2

3

ΨQ : p3, 3q 13

dc : p3, 1q 13

ec, nc : p1, 1q1,0

Lagrangian L “ Lkin. ` LYuk. ` Lpot. ΨQ,L “ pu, d, UqL,Ψ` “ pν, `,NqL:

LYuk. “ ´λu1u1,RΦ:1ΨT,L ´ λu2u2,RΦ:2ΨT,L ´

λd

ΛεijkdbRΦi1Φj2Ψk

T,L

´ λnn1,RΦ:1ΨQ,L ´λe

ΛεijkeRΦi1Φj2Ψk

Q,L ` h.c.,

Lpot. “ µ2Φ1:Φ2 ` h.c.

Hypercharge embedding (diagp1, 1,´2qp2?

3q):

Y “ X ´ T 8?

3 DµΦ “ pBµ ´1

3gXB

Xµ Φ` igWw

µ qΦ


Partial decay widths in LH§ 1-loop decays

ΓphÑ ggqLH „α2sm

3h

32π3v2

ˇ

ˇ

ˇ

ÿ

f,col

´1

2F 1

2pxf q yf

ˇ

ˇ

ˇ

2

ΓphÑ γγqLH „α2m2

h

256π3v2

ˇ

ˇ

ˇ

ÿ

f,ch

4

2F 1

2pxf q yf `

ÿ

v,ch

F1pxvq yv `ÿ

s,ch

F0pxsq ys

ˇ

ˇ

ˇ

2

where xi “4m2

i

m2h

, Fipxiq are loop functions, yi the modified Yuk. coupl.

ñ narrow-width approximation:σLHσSM

pgg Ñ hq “ΓphÑ ggqLHΓphÑ ggqSM

§ tree-level decays

ΓphÑ V V qLH „ ΓphÑ V V qSM

ˆ

ghV VgSMhV V

˙2

ΓphÑ ffqLH „ ΓphÑ ffqSM

ˆ

ghffgSMhff

˙2

where ghV V “m2V

v yV and ghff “mfv yf


Cancellations of Divergencies in Yukawa sector

λt λt`

λT λT`

λT F

9

ż

d4k

p2πq41

k2pk2 ´m2T q

!

λ2t pk

2 ´m2T q ` k

2λ2T ´

mT

FλT k

2)

Little Higgs global symmetry imposes relation

mT

F“λ2t ` λ

2T

λTùñ Quadratic divergence cancels

Collective Symm. break-ing: λt9λ1λ2 , λ1 “ 0or λ2 “ 0 ñ SUp3q ÑrSUp3qs2 Φ1

Φ2

Φ1

Φ2

ΨQ

uc1

uc2

ΨQ „λ2

1λ22

16π2log

ˆ

Λ2

µ2

˙

|Φ:1Φ2|2


Constraints from Oblique Corrections: S, T , U

ZL ZLÝÑ

ZL ZL∆T „ ∆ρ „ ∆M2

ZZ ¨ Z

ZT ZTÝÑ

ZT ZT∆S „W 0

µνBµν ,∆U „W 0

µνW0µν

———————————————————————————————˛ All low-energy effects order v2F 2 (Wilson coefficients)

∆S, ∆T in the Littlest Higgs model, violation of Custodial SU(2): Csáki

et al., 2002; Hewett et al., 2002; Han et al., 2003; Chen/Dawson, 2003; Kilian/JRR, 2003

∆S

8π“ ´

”

c2pc2´s2qg2 `5 c

1 2pc1 2´s1 2qg1 2

ı

v2

F 2 Ñ 0 α∆T Ñ 54v2

F 2 ´2v2λ2

2φ

M4φ

Á v2

F 2

Constraints from contact IA: ( f p3qJJ , f p1qJJ ) 4.5 TeV À F c2 10 TeV À F c1 2

3 Constraints evaded ðñ c, c1 ! 1B1, Z 1,W 1 ˘ superheavy (OpΛq) decouple from fermions

status of little higgs models in 2015reuter/downloads/2015_annecy.pdf1/32j. r. reuter little higgs...

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